Toric degenerations of spherical varieties
By Valery Alexeev, M. Brion. 2004
139 citations recorded by the source corpus.
Abstract.We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by mirror symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provide an explanation for the limits as boundary points of the moduli space of stable pairs whose existence is predicted by the Minimal Model Program.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9e8585d3470b54d4a204b9007b2909cee5ce4b3e
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In Geometry and Topology
- M. Mustaţă
- R. Lazarsfeld
- N. Perrin
- Bernd Sturmfels
- Thibaut Delcroix
- Chi Li
- P. Bougerol
- Neil O'Connell
In Mathematical Physics
- Neil O'Connell
- Bernd Sturmfels
- P. Bougerol
- Ezra Miller
- M. Mustaţă
- R. Lazarsfeld
- Thibaut Delcroix
- Philippe Biane
Citations in the corpus
- Combinatorial Commutative Algebra (2004, background): “A very general result to the effect that every spherical variety degenerates flatly to a toric variety was recently proved by Alexeev and Brion [AB04].”
- Convex Bodies Associated to Linear Series (2008, background): “An analogous polyhedron on spherical varieties has been studied in [10], [34], [1], [25].”
- K-stability of Fano spherical varieties (2016, background): “omogeneous toric bundles. They should be considered as the "most symmetric" spherical varieties. In particular, even if it is possible to degenerate any spherical variety to a toric variety [AB04c], it is at the expense of some symmetries, as it can be made equivariantly only with respect ”
- ON THE GEOMETRY OF SPHERICAL VARIETIES (2012, background): “For spherical varieties, this was first developed by Kaveh [73] and Alexeev and Brion [3] inspired in many aspects by the work of Caldero [43] on toric degeneration of projective rational homogeneous spaces.”
- Continuous crystal and Duistermaat-Heckman measure for Coxeter groups (2008, background): “For a realization of a Coxeter system (W,S), if a closed family B(λ), λ ∈ C̄, of highest weight continuous normal crystals exists, then it is unique.”